I think it depends on why he is a bad breaker. Does he not hit it hard? Does he lose control of the cue ball?
It really comes down to technique for 90% of it. I can break just about as good with a house cue as with my Gilbert...the Gilbert with a Samsara tip just gives me a slight edge.
If they can hit the head ball square most of the time but just can't hit it hard for some reason then I would look for a breaker with a stiff taper, probably a bit lighter weight, and a very hard tip to get every bit of speed out of their stroke. Thinking a BK3.
If they have issues with hitting the head ball square, lose control of the cue ball, and are at any risk of miscuing a lot, then stay away from the phenolic tips. I'd go with a leather break tip like Samsara, a cue that weighs similar to their playing cue and really have them focus on technique and hitting the head ball square, even if they have to pull back on how hard they're hitting. At this point really any solid cue with a stiffish shaft taper and the right tip will be great. I love my Gilbert jump/break but there are lots of good options.
Yup this is about right. They should try lightening up their grip on the break if they haven't already done so, if either speed or accuracy increases that should tell you that they have a long way to go on technique before they think of buying a dedicated break cue. If they swing wild there's no sense buying a $400 cue, any break cue that is actually worth that price (not just priced that high to market it as 'premium') is for someone with a ton of speed and control.
Here's a drill:
First, with your playing cue, set up the balls as shown and just practice lagging the ball into the pocket, with the CB following it in. Then hit a soft stop shot with controlled backspin, the goal being to pocket the ball without touching the points and to freeze the CB dead. Then hit a harder stop shot. It doesn't matter if your power or accuracy is the weak link in your stroke, this requires you to develop both. Work up hitting harder and harder, and then start drawing back until you can bring the CB back where you began. Then switch to your break cue and try to hit the stop shot on this, still using your normal shooting stance, not your break stance. Unless you can hit a ball cleanly enough to do this, there's no point buying an expensive break cue and swinging even wilder for more power, you'll just reinforce bad habits. Then transition more to your break stance and keep the same control with this drill, but don't worry about using full power at first.
That's the kind of accuracy you should aiming for on the break, every time. Hit the head ball that dead-on aiming to drive it through the rack to your preferred spot in the back/side of the rack. Many people waste half their cue energy with unintentional sidespin on the CB and not hitting the head ball square, and not realizing this, just keep trying to hit it harder, which makes their accuracy go down further, and it's just a cycle of diminishing returns. I see 110 lb women league players break better than big hulking guys putting everything they have into it all the time.
Control is everything. When you try to hit harder than you can control, you lose power. Even if you have a weak swing, it's a mistake to try to make up for that power if that costs you any control at all.